Natural selection is a process by which the genotypes in a population that are best adapted to the environment increase in frequency relative to less well-adapted genotypes over a number of generations. It is a process by which biological populations are altered over time, as a result of the propagation of heritable traits that affect the capacity of individual organisms to survive and reproduce. This process is based on competitive situation: many individuals are in selfish competition with each other, and in this struggle of existence, only the fittest survive and reproduce themselves successfully (survival of the fittest).
The idea of natural selection is basically a metaphor: nature selects organisms in a natural way similar to artificial selection in breeding, where animals and plants with traits considered desirable by human breeders are systematically favored for reproduction. The basic idea is simple: changes in any organism's makeup or behavior will persist or not according to whether they make it more or less likely for that organism and its descendants to survive. Natural selection leads to an adaptation and accommodation of a species to a certain ecological or economic niche. According to John H. Holland, natural selection can be considered as a selection of persistent combinations from the sea of possibilities:
- "If we equate simplicity to a limited number of "building blocks" (atoms, nucleotides, linguistic phonemes, computer instructions) and complexity to the vast number of ways of combining those building blocks (molecules, DNA, speech, programs), then we open the possibility of deriving complexity from simplicity. Darwinian selection is, from one point of view, the selection of persistent combinations" 
The concept of natural selection can be meaningful applied to other units of selection, often characterized by different scopes and levels, see Kin Selection, Group Selection and Multilevel Selection, if these levels are influenced by replicators. Natural selection acts on the genotype and selects always something which is replicated. This replicator can be a gene or meme.
According to Terry Deacon, relaxed selection is a special form of natural selection, where the selection pressure and the competition is low (i.e. where natural selection itself is nearly absent), and the variety of traits which are able to survive and reproduce is high. When the selection pressures lift, genomes go wandering and new, unexpected traits may arise. I think if there is a "relaxed selection", then it one can also speak of a "fierce selection": a natural selection with fierce competition when the climate is harsh and the food is sparse. Under this conditions only the best, well adapted individuals survive.
Does natural selection occur in different degrees? According to Nicholas S. Thompson, Emeritus Professor of Psychology and Ethology, Clark University, this kind of selection would be associated with expansion and contraction of populations: rapid expansion of populations (when selection is relaxed) vs. rapid contraction of populations (when selection is intensified).
- During "relaxed selection" or "facilitated variation", the system enters an exploration phase: the chances of finding new configurations, traits and features are higher. The selection pressure for a species to remain in the corresponding niche is lower. The population is expanding and growing rapidly. Variation is facilitated.
- During "fierce selection" or "impeded variation", the system enters an exploitation phase: chances of optimizing existing configurations, traits and features are higher. The selection pressure for a species to remain in the corresponding niche is higher. The population is contracting and shrinking rapidly. Variation is impeded.
- Christine Kenneally, "As if from nowhere", New Scientist 27 Sep 2008 (article about the topic of "relaxed selection", a concept invented by Terry Deacon. Terry Deacon is an anthropology professor at Berkeley)
- Wikipedia Entry for Natural Selection
- Seed Magazine article about human evolution and relaxed selection